How do you find the roots, real and imaginary, of y= -2(x+1)^2+(-x-2)^2 using the quadratic formula?

1 Answer
Jan 5, 2016

Form a quadratic equation, and solve it. Method below first, solution underneath.

Explanation:

Method

Start by writing your equation in the form:
y=ax^2+bx+c

The roots are when y=0
So you will have a quadratic equation of the form:
ax^2+bx+c=0

Then use the quadratic formula:

x=(-bpmsqrt(b^2-4ac))/(2a)

Which can give two roots due to the pmsquare root.

Solution

y=-x^2+0x+2

for roots, y=0

-x^2+0x+2=0

a=-1, b=0, c=2

so

x=(pmsqrt(8))/(-2)=pmsqrt2

x=sqrt2

or

x=-sqrt2